Geoscience Reference
In-Depth Information
Figure 10.5
Leafy vegetation: (a) without and (b) with flow shear.
For a group of homogeneous vegetation elements, the total projected area per unit
area is defined as the product of the vegetation density and the projected area of
an individual stem,
N
a
A
v
. However, in natural cases, vegetation elements may be
heterogeneous, and thus the sum of the projected areas of all elements,
i
A
vi
,is
often considered. Here,
A
vi
is the project area of the individual vegetation element
numbered as
i
.
Vegetation concentration
Consider a control volume extending from the stream bed to the water surface and
holding the mixture of the water and a group of vegetation stems, as shown in Fig. 10.4.
The volumetric concentration of vegetation,
c
v
, is defined as the ratio of the volume
of vegetation to the total volume of the mixture. For homogeneous, rigid vegetation,
c
v
can be expressed as
D
2
min
N
a
π
(
)
h
v
,
h
c
v
=
(10.4)
4
h
Note that
c
v
is the vegetation concentration averaged over the entire flow depth.
Naturally, the local concentration of vegetation in the vegetation layer is defined as
D
2
4
N
a
π
c
v
0
=
(10.5)
For the emergent vegetation shown in Fig. 4(a),
c
v
=
c
v
0
, and for the submerged
vegetation shown in Fig. 4(b),
c
v
=
c
v
0
h
v
/
h
.
